%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP160^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:08:36 AM UTC 2026
% Result : Theorem 1.42s 0.59s
% Output : Refutation 1.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP160^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n013.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 20:03:21 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.22/0.32 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.68/0.52 % (2592157)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.68/0.52 % (2592162)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2493228393:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.68/0.52 % (2592164)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=762977803:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.68/0.52 % (2592163)lrs+10_16_si=on:nwc=1.5:random_seed=3959613093:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.68/0.52 % (2592164)Instruction limit reached!
% 0.68/0.52 % (2592164)------------------------------
% 0.68/0.52 % (2592164)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.52 % (2592164)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.52 % (2592164)CaDiCaL version: 2.1.3
% 0.68/0.52 % (2592164)Termination reason: Instruction limit
% 0.68/0.52 % (2592164)Termination phase: shuffling
% 0.68/0.52 % (2592164)Time elapsed: 0.003 s
% 0.68/0.52 % (2592164)Peak memory usage: 10 MB
% 0.68/0.52 % (2592164)Instructions burned: 5 (million)
% 0.68/0.52 % (2592163)Instruction limit reached!
% 0.68/0.52 % (2592163)------------------------------
% 0.68/0.52 % (2592163)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.52 % (2592163)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.52 % (2592163)CaDiCaL version: 2.1.3
% 0.68/0.52 % (2592163)Termination reason: Instruction limit
% 0.68/0.52 % (2592163)Termination phase: shuffling
% 0.68/0.52 % (2592163)Time elapsed: 0.009 s
% 0.68/0.52 % (2592163)Peak memory usage: 10 MB
% 0.68/0.52 % (2592163)Instructions burned: 20 (million)
% 0.68/0.52 % (2592162)Instruction limit reached!
% 0.68/0.52 % (2592162)------------------------------
% 0.68/0.52 % (2592162)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.52 % (2592162)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.52 % (2592162)CaDiCaL version: 2.1.3
% 0.68/0.52 % (2592162)Termination reason: Instruction limit
% 0.68/0.52 % (2592162)Termination phase: SInE selection
% 0.68/0.52 % (2592162)Time elapsed: 0.022 s
% 0.68/0.52 % (2592162)Peak memory usage: 12 MB
% 0.68/0.52 % (2592162)Instructions burned: 90 (million)
% 0.68/0.52 % (2592165)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=2734466736:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.68/0.52 % (2592175)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.68/0.52 % (2592175)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=798647169:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.68/0.52 % (2592172)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1904961246:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.68/0.52 % (2592172)Instruction limit reached!
% 0.68/0.52 % (2592172)------------------------------
% 0.68/0.52 % (2592172)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.52 % (2592172)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.52 % (2592172)CaDiCaL version: 2.1.3
% 0.68/0.52 % (2592172)Termination reason: Instruction limit
% 0.68/0.52 % (2592172)Termination phase: shuffling
% 0.68/0.52 % (2592172)Time elapsed: 0.002 s
% 0.68/0.52 % (2592172)Peak memory usage: 10 MB
% 0.68/0.52 % (2592172)Instructions burned: 3 (million)
% 0.68/0.52 % (2592175)Instruction limit reached!
% 0.68/0.52 % (2592175)------------------------------
% 0.68/0.52 % (2592175)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.52 % (2592175)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.52 % (2592175)CaDiCaL version: 2.1.3
% 0.68/0.52 % (2592175)Termination reason: Instruction limit
% 0.68/0.52 % (2592175)Termination phase: shuffling
% 0.68/0.52 % (2592175)Time elapsed: 0.003 s
% 0.68/0.52 % (2592175)Peak memory usage: 10 MB
% 0.68/0.52 % (2592175)Instructions burned: 10 (million)
% 0.68/0.52 % (2592178)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=462106969:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.68/0.56 % (2592178)Instruction limit reached!
% 0.68/0.56 % (2592178)------------------------------
% 0.68/0.56 % (2592178)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.56 % (2592178)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.56 % (2592178)CaDiCaL version: 2.1.3
% 0.68/0.56 % (2592178)Termination reason: Instruction limit
% 0.68/0.56 % (2592178)Termination phase: shuffling
% 0.68/0.56 % (2592178)Time elapsed: 0.004 s
% 0.68/0.56 % (2592178)Peak memory usage: 10 MB
% 0.68/0.56 % (2592178)Instructions burned: 14 (million)
% 0.68/0.56 % (2592167)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3016804713:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.68/0.56 % (2592166)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1731908248:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.68/0.56 % (2592179)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.68/0.56 % (2592179)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.68/0.56 % (2592168)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.68/0.56 % (2592168)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.68/0.56 % (2592168)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=4051465756:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.68/0.56 % (2592173)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=668860543:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.68/0.56 % (2592173)Instruction limit reached!
% 0.68/0.56 % (2592173)------------------------------
% 0.68/0.56 % (2592173)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.56 % (2592173)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.56 % (2592173)CaDiCaL version: 2.1.3
% 0.68/0.56 % (2592173)Termination reason: Instruction limit
% 0.68/0.56 % (2592173)Termination phase: shuffling
% 0.68/0.56 % (2592173)Time elapsed: 0.003 s
% 0.68/0.56 % (2592173)Peak memory usage: 10 MB
% 0.68/0.56 % (2592173)Instructions burned: 5 (million)
% 0.68/0.56 % (2592179)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3712352863:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.68/0.56 % (2592181)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=850408669:i=86:piset=equals:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/86Mi)
% 0.68/0.56 % (2592166)Instruction limit reached!
% 0.68/0.56 % (2592166)------------------------------
% 0.68/0.56 % (2592166)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.56 % (2592166)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.56 % (2592166)CaDiCaL version: 2.1.3
% 0.68/0.56 % (2592166)Termination reason: Instruction limit
% 0.68/0.56 % (2592166)Termination phase: shuffling
% 0.68/0.56 % (2592166)Time elapsed: 0.033 s
% 0.68/0.56 % (2592166)Peak memory usage: 10 MB
% 0.68/0.56 % (2592166)Instructions burned: 25 (million)
% 0.68/0.56 % (2592179)Instruction limit reached!
% 0.68/0.56 % (2592179)------------------------------
% 0.68/0.56 % (2592179)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.56 % (2592179)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.56 % (2592179)CaDiCaL version: 2.1.3
% 0.68/0.56 % (2592179)Termination reason: Instruction limit
% 0.68/0.56 % (2592179)Termination phase: shuffling
% 0.68/0.56 % (2592179)Time elapsed: 0.026 s
% 0.68/0.56 % (2592179)Peak memory usage: 11 MB
% 0.68/0.56 % (2592179)Instructions burned: 29 (million)
% 0.68/0.56 % (2592167)Instruction limit reached!
% 0.68/0.56 % (2592167)------------------------------
% 0.68/0.56 % (2592167)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.59 % (2592167)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.59 % (2592167)CaDiCaL version: 2.1.3
% 1.42/0.59 % (2592167)Termination reason: Instruction limit
% 1.42/0.59 % (2592167)Termination phase: Property scanning
% 1.42/0.59 % (2592167)Time elapsed: 0.042 s
% 1.42/0.59 % (2592167)Peak memory usage: 11 MB
% 1.42/0.59 % (2592167)Instructions burned: 75 (million)
% 1.42/0.59 % (2592181)Instruction limit reached!
% 1.42/0.59 % (2592181)------------------------------
% 1.42/0.59 % (2592181)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.59 % (2592181)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.59 % (2592181)CaDiCaL version: 2.1.3
% 1.42/0.59 % (2592181)Termination reason: Instruction limit
% 1.42/0.59 % (2592181)Termination phase: Preprocessing 1
% 1.42/0.59 % (2592181)Time elapsed: 0.021 s
% 1.42/0.59 % (2592181)Peak memory usage: 11 MB
% 1.42/0.59 % (2592181)Instructions burned: 87 (million)
% 1.42/0.59 % (2592187)lrs+10_1_si=on:cs=on:random_seed=3707962969:i=8:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.42/0.59 % (2592189)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.42/0.59 % (2592189)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=1580624312:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.42/0.59 % (2592189)Instruction limit reached!
% 1.42/0.59 % (2592189)------------------------------
% 1.42/0.59 % (2592189)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.59 % (2592189)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.59 % (2592189)CaDiCaL version: 2.1.3
% 1.42/0.59 % (2592189)Termination reason: Instruction limit
% 1.42/0.59 % (2592189)Termination phase: shuffling
% 1.42/0.59 % (2592189)Time elapsed: 0.003 s
% 1.42/0.59 % (2592189)Peak memory usage: 10 MB
% 1.42/0.59 % (2592189)Instructions burned: 4 (million)
% 1.42/0.59 % (2592190)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=204076957:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 1.42/0.59 % (2592187)Instruction limit reached!
% 1.42/0.59 % (2592187)------------------------------
% 1.42/0.59 % (2592187)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.59 % (2592187)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.59 % (2592187)CaDiCaL version: 2.1.3
% 1.42/0.59 % (2592187)Termination reason: Instruction limit
% 1.42/0.59 % (2592187)Termination phase: shuffling
% 1.42/0.59 % (2592187)Time elapsed: 0.008 s
% 1.42/0.59 % (2592187)Peak memory usage: 10 MB
% 1.42/0.59 % (2592187)Instructions burned: 8 (million)
% 1.42/0.59 % (2592192)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3187083344:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.42/0.59 % (2592192)Instruction limit reached!
% 1.42/0.59 % (2592192)------------------------------
% 1.42/0.59 % (2592192)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.59 % (2592192)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.59 % (2592192)CaDiCaL version: 2.1.3
% 1.42/0.59 % (2592192)Termination reason: Instruction limit
% 1.42/0.59 % (2592192)Termination phase: shuffling
% 1.42/0.59 % (2592192)Time elapsed: 0.007 s
% 1.42/0.59 % (2592192)Peak memory usage: 10 MB
% 1.42/0.59 % (2592192)Instructions burned: 28 (million)
% 1.42/0.59 % (2592191)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2391768627:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.42/0.59 % (2592190)Instruction limit reached!
% 1.42/0.59 % (2592190)------------------------------
% 1.42/0.59 % (2592190)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.59 % (2592190)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.59 % (2592190)CaDiCaL version: 2.1.3
% 1.42/0.59 % (2592190)Termination reason: Instruction limit
% 1.42/0.59 % (2592190)Termination phase: shuffling
% 1.42/0.59 % (2592190)Time elapsed: 0.017 s
% 1.42/0.59 % (2592190)Peak memory usage: 11 MB
% 1.42/0.59 % (2592190)Instructions burned: 39 (million)
% 1.42/0.59 % (2592199)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=1185897096:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.42/0.59 % (2592195)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2279031309:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.42/0.59 % (2592199)Instruction limit reached!
% 1.42/0.59 % (2592199)------------------------------
% 1.42/0.59 % (2592199)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.59 % (2592199)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.59 % (2592199)CaDiCaL version: 2.1.3
% 1.42/0.59 % (2592199)Termination reason: Instruction limit
% 1.42/0.59 % (2592199)Termination phase: shuffling
% 1.42/0.59 % (2592199)Time elapsed: 0.004 s
% 1.42/0.59 % (2592199)Peak memory usage: 10 MB
% 1.42/0.59 % (2592199)Instructions burned: 15 (million)
% 1.42/0.59 % (2592195)Instruction limit reached!
% 1.42/0.59 % (2592195)------------------------------
% 1.42/0.59 % (2592195)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.59 % (2592195)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.59 % (2592195)CaDiCaL version: 2.1.3
% 1.42/0.59 % (2592195)Termination reason: Instruction limit
% 1.42/0.59 % (2592195)Termination phase: shuffling
% 1.42/0.59 % (2592195)Time elapsed: 0.007 s
% 1.42/0.59 % (2592195)Peak memory usage: 10 MB
% 1.42/0.59 % (2592195)Instructions burned: 17 (million)
% 1.42/0.59 % (2592204)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3906744992:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.42/0.59 % (2592198)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2896440523:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.42/0.59 % (2592203)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=642435941:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.42/0.59 % (2592203)Instruction limit reached!
% 1.42/0.59 % (2592203)------------------------------
% 1.42/0.59 % (2592203)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.59 % (2592203)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.59 % (2592203)CaDiCaL version: 2.1.3
% 1.42/0.59 % (2592203)Termination reason: Instruction limit
% 1.42/0.59 % (2592203)Termination phase: shuffling
% 1.42/0.59 % (2592203)Time elapsed: 0.002 s
% 1.42/0.59 % (2592203)Peak memory usage: 10 MB
% 1.42/0.59 % (2592203)Instructions burned: 3 (million)
% 1.42/0.59 % (2592204)Instruction limit reached!
% 1.42/0.59 % (2592204)------------------------------
% 1.42/0.59 % (2592204)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.59 % (2592204)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.59 % (2592204)CaDiCaL version: 2.1.3
% 1.42/0.59 % (2592204)Termination reason: Instruction limit
% 1.42/0.59 % (2592204)Termination phase: shuffling
% 1.42/0.59 % (2592204)Time elapsed: 0.008 s
% 1.42/0.59 % (2592204)Peak memory usage: 11 MB
% 1.42/0.59 % (2592204)Instructions burned: 31 (million)
% 1.42/0.59 % (2592205)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=2856319147:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.42/0.59 % (2592210)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.42/0.59 % (2592210)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.42/0.59 % (2592210)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=3292050747:i=14:add=off:nm=40:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/14Mi)
% 1.42/0.59 % (2592210)Instruction limit reached!
% 1.42/0.59 % (2592210)------------------------------
% 1.42/0.59 % (2592210)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.59 % (2592210)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.59 % (2592210)CaDiCaL version: 2.1.3
% 1.42/0.59 % (2592210)Termination reason: Instruction limit
% 1.42/0.59 % (2592210)Termination phase: shuffling
% 1.42/0.59 % (2592210)Time elapsed: 0.007 s
% 1.42/0.59 % (2592210)Peak memory usage: 11 MB
% 1.42/0.59 % (2592210)Instructions burned: 27 (million)
% 1.42/0.59 % (2592205)Instruction limit reached!
% 1.42/0.59 % (2592205)------------------------------
% 1.42/0.59 % (2592205)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.59 % (2592205)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.59 % (2592205)CaDiCaL version: 2.1.3
% 1.42/0.59 % (2592205)Termination reason: Instruction limit
% 1.42/0.59 % (2592205)Termination phase: shuffling
% 1.42/0.59 % (2592205)Time elapsed: 0.013 s
% 1.42/0.59 % (2592205)Peak memory usage: 10 MB
% 1.42/0.59 % (2592205)Instructions burned: 29 (million)
% 1.42/0.59 % (2592213)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.42/0.59 % (2592213)lrs+1010_4:1_slsqr=8,1:to=kbo:cha=on:drc=off:si=on:sp=arity:lcm=predicate:uwa=off:fd=preordered:gs=on:nwc=5:s2agt=32:slsqc=1:kmz=on:updr=off:chr=on:pe=on:slsq=on:random_seed=3274627387:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2997 on theBenchmark for (2997ds/8Mi)
% 1.42/0.59 % (2592213)Instruction limit reached!
% 1.42/0.59 % (2592213)------------------------------
% 1.42/0.59 % (2592213)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.59 % (2592213)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.59 % (2592213)CaDiCaL version: 2.1.3
% 1.42/0.59 % (2592213)Termination reason: Instruction limit
% 1.42/0.59 % (2592213)Termination phase: shuffling
% 1.42/0.59 % (2592213)Time elapsed: 0.002 s
% 1.42/0.59 % (2592213)Peak memory usage: 10 MB
% 1.42/0.59 % (2592213)Instructions burned: 9 (million)
% 1.42/0.59 % (2592209)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=662671101:cond=on:i=60:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/60Mi)
% 1.42/0.59 % (2592191) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2592157-2592191"...
% 1.42/0.59 % (2592168)Instruction limit reached!
% 1.42/0.59 % (2592168)------------------------------
% 1.42/0.59 % (2592168)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.59 % (2592168)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.59 % (2592168)CaDiCaL version: 2.1.3
% 1.42/0.59 % (2592168)Termination reason: Instruction limit
% 1.42/0.59 % (2592168)Termination phase: Function definition elimination
% 1.42/0.59 % (2592168)Time elapsed: 0.135 s
% 1.42/0.59 % (2592168)Peak memory usage: 13 MB
% 1.42/0.59 % (2592214)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=1775177240:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2997 on theBenchmark for (2997ds/31Mi)
% 1.42/0.59 % (2592168)Instructions burned: 158 (million)
% 1.42/0.59 % (2592191)...printing done.
% 1.42/0.59 % (2592191)Refutation found. Thanks to Tanya!
% 1.42/0.59 % SZS status Theorem for theBenchmark
% 1.42/0.59 % SZS output start Proof for theBenchmark
% 1.42/0.59 thf(type_def_5, type, refine1665802226e_nres: $tType > $tType).
% 1.42/0.59 thf(type_def_6, type, autoref_annot: $tType).
% 1.42/0.59 thf(type_def_7, type, product_prod: ($tType * $tType) > $tType).
% 1.42/0.59 thf(type_def_8, type, set: $tType > $tType).
% 1.42/0.59 thf(type_def_9, type, nat: $tType).
% 1.42/0.59 thf(type_def_10, type, int: $tType).
% 1.42/0.59 thf(type_def_11, type, d: $tType).
% 1.42/0.59 thf(type_def_12, type, c: $tType).
% 1.42/0.59 thf(type_def_13, type, b: $tType).
% 1.42/0.59 thf(type_def_14, type, a: $tType).
% 1.42/0.59 thf(type_def_15, type, sTfun: ($tType * $tType) > $tType).
% 1.42/0.59 thf(func_def_0, type, type: !>[X0: $tType]:($o)).
% 1.42/0.59 thf(func_def_1, type, ord: !>[X0: $tType]:($o)).
% 1.42/0.59 thf(func_def_2, type, order: !>[X0: $tType]:($o)).
% 1.42/0.59 thf(func_def_3, type, linorder: !>[X0: $tType]:($o)).
% 1.42/0.59 thf(func_def_4, type, preorder: !>[X0: $tType]:($o)).
% 1.42/0.59 thf(func_def_5, type, autoref_ANNOT: !>[X0: $tType]:((X0 > autoref_annot > X0))).
% 1.42/0.59 thf(func_def_6, type, autoref_APP: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0 > X1))).
% 1.42/0.59 thf(func_def_7, type, autoref_OP: !>[X0: $tType]:((X0 > X0))).
% 1.42/0.59 thf(func_def_8, type, autoref_rel_annot: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > autoref_annot))).
% 1.42/0.59 thf(func_def_9, type, autore2013370551TERNAL: !>[X0: $tType]:((X0 > X0))).
% 1.42/0.59 thf(func_def_10, type, autore813025987NAL_EQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 1.42/0.59 thf(func_def_11, type, comp: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > (X2 > X0) > X2 > X1))).
% 1.42/0.59 thf(func_def_12, type, fun_upd: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0 > X1 > X0 > X1))).
% 1.42/0.59 thf(func_def_13, type, id: !>[X0: $tType]:((X0 > X0))).
% 1.42/0.59 thf(func_def_14, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 1.42/0.59 thf(func_def_15, type, all_interval_nat: ((nat > $o) > nat > nat > $o)).
% 1.42/0.59 thf(func_def_16, type, uncurry: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 1.42/0.59 thf(func_def_17, type, case_nat: !>[X0: $tType]:((X0 > (nat > X0) > nat > X0))).
% 1.42/0.59 thf(func_def_18, type, rec_nat: !>[X0: $tType]:((X0 > (nat > X0 > X0) > nat > X0))).
% 1.42/0.59 thf(func_def_19, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 1.42/0.59 thf(func_def_20, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 1.42/0.59 thf(func_def_21, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 1.42/0.59 thf(func_def_22, type, product_apfst: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > product_prod @ X0 @ X2 > product_prod @ X1 @ X2))).
% 1.42/0.59 thf(func_def_23, type, product_apsnd: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > product_prod @ X2 @ X0 > product_prod @ X2 @ X1))).
% 1.42/0.59 thf(func_def_24, type, product_case_bool: !>[X0: $tType]:((X0 > X0 > $o > X0))).
% 1.42/0.59 thf(func_def_25, type, product_curry: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X0 @ X1 > X2) > X0 > X1 > X2))).
% 1.42/0.59 thf(func_def_26, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 1.42/0.59 thf(func_def_27, type, product_map_prod: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X0 > X1) > (X2 > X3) > product_prod @ X0 @ X2 > product_prod @ X1 @ X3))).
% 1.42/0.59 thf(func_def_28, type, product_rec_bool: !>[X0: $tType]:((X0 > X0 > $o > X0))).
% 1.42/0.59 thf(func_def_29, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 1.42/0.59 thf(func_def_30, type, product_case_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 1.42/0.59 thf(func_def_31, type, product_fst: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 1.42/0.59 thf(func_def_32, type, product_snd: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 1.42/0.59 thf(func_def_33, type, product_swap: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > product_prod @ X1 @ X0))).
% 1.42/0.59 thf(func_def_34, type, refine1687780735RETURN: !>[X0: $tType]:((X0 > refine1665802226e_nres @ X0))).
% 1.42/0.59 thf(func_def_35, type, refine463715084e_bind: !>[X0: $tType, X1: $tType]:((refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1))).
% 1.42/0.59 thf(func_def_36, type, refine1580981607t_assn: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > (X1 > $o) > X0 > $o))).
% 1.42/0.59 thf(func_def_37, type, refine476890328es_rel: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > set @ product_prod @ refine1665802226e_nres @ X0 @ refine1665802226e_nres @ X1))).
% 1.42/0.59 thf(func_def_38, type, refine171938416RT_bnd: !>[X0: $tType]:(($o > refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0))).
% 1.42/0.59 thf(func_def_39, type, refine1361002633n_bool: set @ product_prod @ $o @ $o).
% 1.42/0.59 thf(func_def_40, type, id2: !>[X0: $tType]:(set @ product_prod @ X0 @ X0)).
% 1.42/0.59 thf(func_def_41, type, fun_rel: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((set @ product_prod @ X0 @ X1 > set @ product_prod @ X2 @ X3 > set @ product_prod @ (X0 > X2) @ (X1 > X3)))).
% 1.42/0.59 thf(func_def_42, type, prod_rel: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((set @ product_prod @ X0 @ X1 > set @ product_prod @ X2 @ X3 > set @ product_prod @ product_prod @ X0 @ X2 @ product_prod @ X1 @ X3))).
% 1.42/0.59 thf(func_def_43, type, relAPP: !>[X0: $tType, X1: $tType, X2: $tType]:(((set @ product_prod @ X0 @ X1 > X2) > set @ product_prod @ X0 @ X1 > X2))).
% 1.42/0.59 thf(func_def_44, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 1.42/0.59 thf(func_def_45, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 1.42/0.59 thf(func_def_46, type, r1: set @ product_prod @ a @ c).
% 1.42/0.59 thf(func_def_47, type, r2: set @ product_prod @ b @ d).
% 1.42/0.59 thf(func_def_49, type, vIMP: ($o > $o > $o)).
% 1.42/0.59 thf(func_def_50, type, vNOT: ($o > $o)).
% 1.42/0.59 thf(func_def_51, type, vOR: ($o > $o > $o)).
% 1.42/0.59 thf(func_def_52, type, vAND: ($o > $o > $o)).
% 1.42/0.59 thf(func_def_55, type, db1: !>[X0: $tType]:(X0)).
% 1.42/0.59 thf(func_def_56, type, db0: !>[X0: $tType]:(X0)).
% 1.42/0.59 thf(func_def_57, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 1.42/0.59 thf(func_def_58, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 1.42/0.59 thf(func_def_59, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 1.42/0.59 thf(func_def_60, type, db2: !>[X0: $tType]:(X0)).
% 1.42/0.59 thf(func_def_61, type, db3: !>[X0: $tType]:(X0)).
% 1.42/0.59 thf(func_def_62, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 1.42/0.59 thf(func_def_63, type, sK0: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X2 @ product_prod @ X4 @ X3 > X4))).
% 1.42/0.59 thf(func_def_64, type, sK1: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X2 @ product_prod @ X4 @ X3 > X1))).
% 1.42/0.59 thf(func_def_65, type, sK2: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X2 @ product_prod @ X4 @ X3 > X0))).
% 1.42/0.59 thf(func_def_66, type, sK3: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X2 @ product_prod @ X4 @ X3 > X2))).
% 1.42/0.59 thf(func_def_67, type, sK4: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X2 @ product_prod @ X4 @ X3 > X3))).
% 1.42/0.59 thf(func_def_68, type, sK5: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 1.42/0.59 thf(func_def_69, type, sK6: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 1.42/0.59 thf(func_def_70, type, sK7: !>[X0: $tType, X1: $tType]:((((X0 > X1) > product_prod @ X0 @ X0 > $o) > X0))).
% 1.42/0.59 thf(func_def_71, type, sK8: !>[X0: $tType, X1: $tType]:((((X0 > X1) > product_prod @ X0 @ X0 > $o) > X0 > X1))).
% 1.42/0.59 thf(func_def_72, type, sK9: !>[X0: $tType, X1: $tType]:((((X0 > X1) > product_prod @ X0 @ X0 > $o) > X0))).
% 1.42/0.59 thf(func_def_73, type, sK10: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 1.42/0.59 thf(func_def_74, type, sK11: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 1.42/0.59 thf(func_def_75, type, sK12: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 1.42/0.59 thf(func_def_76, type, sK13: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X1 @ product_prod @ X5 @ X3 > $o) > X3))).
% 1.42/0.59 thf(func_def_77, type, sK14: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X1 @ product_prod @ X5 @ X3 > $o) > X0))).
% 1.42/0.59 thf(func_def_78, type, sK15: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X1 @ product_prod @ X5 @ X3 > $o) > X2))).
% 1.42/0.59 thf(func_def_79, type, sK16: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X1 @ product_prod @ X5 @ X3 > $o) > X5))).
% 1.42/0.59 thf(func_def_80, type, sK17: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X1 @ product_prod @ X5 @ X3 > $o) > X4))).
% 1.42/0.59 thf(func_def_81, type, sK18: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X1 @ product_prod @ X5 @ X3 > $o) > X1))).
% 1.42/0.59 thf(func_def_82, type, sK19: !>[X0: $tType, X1: $tType]:((product_prod @ (X1 > X0) @ product_prod @ X1 @ X1 > X1))).
% 1.42/0.59 thf(func_def_83, type, sK20: !>[X0: $tType, X1: $tType]:((product_prod @ (X1 > X0) @ product_prod @ X1 @ X1 > X1 > X0))).
% 1.42/0.59 thf(func_def_84, type, sK21: !>[X0: $tType, X1: $tType]:((product_prod @ (X1 > X0) @ product_prod @ X1 @ X1 > X1))).
% 1.42/0.59 thf(func_def_85, type, sK22: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X1))).
% 1.42/0.59 thf(func_def_86, type, sK23: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X0))).
% 1.42/0.59 thf(func_def_87, type, sK24: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X1 @ product_prod @ X2 @ X0 > $o) > X0))).
% 1.42/0.59 thf(func_def_88, type, sK25: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X1 @ product_prod @ X2 @ X0 > $o) > X2))).
% 1.42/0.59 thf(func_def_89, type, sK26: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X1 @ product_prod @ X2 @ X0 > $o) > X1))).
% 1.42/0.59 thf(func_def_90, type, sK27: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X2 @ product_prod @ X0 @ product_prod @ X1 @ X3 > X3))).
% 1.42/0.59 thf(func_def_91, type, sK28: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X2 @ product_prod @ X0 @ product_prod @ X1 @ X3 > X2))).
% 1.42/0.59 thf(func_def_92, type, sK29: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X2 @ product_prod @ X0 @ product_prod @ X1 @ X3 > X1))).
% 1.42/0.59 thf(func_def_93, type, sK30: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X2 @ product_prod @ X0 @ product_prod @ X1 @ X3 > X0))).
% 1.42/0.59 thf(func_def_94, type, sK31: !>[X0: $tType, X1: $tType]:(((X1 > refine1665802226e_nres @ X0) > (X1 > refine1665802226e_nres @ X0) > refine1665802226e_nres @ X1 > X1))).
% 1.42/0.59 thf(func_def_95, type, sK32: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((set @ product_prod @ X3 @ X2 > (X3 > X1) > set @ product_prod @ X1 @ X0 > (X2 > X0) > X3))).
% 1.42/0.59 thf(func_def_96, type, sK33: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((set @ product_prod @ X3 @ X2 > (X3 > X1) > set @ product_prod @ X1 @ X0 > (X2 > X0) > X2))).
% 1.42/0.59 thf(func_def_97, type, sK34: !>[X0: $tType, X1: $tType]:(((X0 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X1) > X0))).
% 1.42/0.59 thf(func_def_98, type, sK35: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X0 @ X1 > X2))).
% 1.42/0.59 thf(func_def_99, type, sK36: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X0 @ X1 > X0))).
% 1.42/0.59 thf(func_def_100, type, sK37: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X0 @ X1 > X1))).
% 1.42/0.59 thf(func_def_101, type, sK38: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 1.42/0.59 thf(func_def_102, type, sK39: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 1.42/0.59 thf(func_def_103, type, sK40: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X6 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X5 @ X2 > $o) > X1))).
% 1.42/0.59 thf(func_def_104, type, sK41: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X6 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X5 @ X2 > $o) > X6))).
% 1.42/0.59 thf(func_def_105, type, sK42: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X6 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X5 @ X2 > $o) > X4))).
% 1.42/0.59 thf(func_def_106, type, sK43: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X6 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X5 @ X2 > $o) > X5))).
% 1.42/0.59 thf(func_def_107, type, sK44: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X6 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X5 @ X2 > $o) > X0))).
% 1.42/0.59 thf(func_def_108, type, sK45: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X6 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X5 @ X2 > $o) > X3))).
% 1.42/0.59 thf(func_def_109, type, sK46: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X6 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X5 @ X2 > $o) > X2))).
% 1.42/0.59 thf(func_def_110, type, sK47: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X2 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X3 @ X4 > X4))).
% 1.42/0.59 thf(func_def_111, type, sK48: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X2 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X3 @ X4 > X3))).
% 1.42/0.59 thf(func_def_112, type, sK49: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X2 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X3 @ X4 > X2))).
% 1.42/0.59 thf(func_def_113, type, sK50: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X2 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X3 @ X4 > X1))).
% 1.42/0.59 thf(func_def_114, type, sK51: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X2 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X3 @ X4 > X0))).
% 1.42/0.59 thf(func_def_115, type, sK52: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X2 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X3 @ X4 > X5))).
% 1.42/0.59 thf(func_def_116, type, sK53: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > (X1 > X0 > $o) > X1))).
% 1.42/0.59 thf(func_def_117, type, sK54: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > (X1 > X0 > $o) > X0))).
% 1.42/0.59 thf(func_def_118, type, sK55: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X6 @ product_prod @ X4 @ X5 > X3))).
% 1.42/0.59 thf(func_def_119, type, sK56: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X6 @ product_prod @ X4 @ X5 > X4))).
% 1.42/0.59 thf(func_def_120, type, sK57: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X6 @ product_prod @ X4 @ X5 > X5))).
% 1.42/0.59 thf(func_def_121, type, sK58: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X6 @ product_prod @ X4 @ X5 > X6))).
% 1.42/0.59 thf(func_def_122, type, sK59: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X6 @ product_prod @ X4 @ X5 > X1))).
% 1.42/0.59 thf(func_def_123, type, sK60: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X6 @ product_prod @ X4 @ X5 > X2))).
% 1.42/0.59 thf(func_def_124, type, sK61: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X6 @ product_prod @ X4 @ X5 > X0))).
% 1.42/0.59 thf(func_def_125, type, sK62: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X2 @ product_prod @ X3 @ product_prod @ X0 @ X1 > $o) > X1))).
% 1.42/0.59 thf(func_def_126, type, sK63: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X2 @ product_prod @ X3 @ product_prod @ X0 @ X1 > $o) > X3))).
% 1.42/0.59 thf(func_def_127, type, sK64: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X2 @ product_prod @ X3 @ product_prod @ X0 @ X1 > $o) > X2))).
% 1.42/0.59 thf(func_def_128, type, sK65: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X2 @ product_prod @ X3 @ product_prod @ X0 @ X1 > $o) > X0))).
% 1.42/0.59 thf(func_def_129, type, sK66: !>[X0: $tType]:((product_prod @ X0 @ X0 > X0))).
% 1.42/0.59 thf(func_def_130, type, sK67: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X1 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ X0 > $o) > X1))).
% 1.42/0.59 thf(func_def_131, type, sK68: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X1 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ X0 > $o) > X0))).
% 1.42/0.59 thf(func_def_132, type, sK69: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X1 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ X0 > $o) > X2))).
% 1.42/0.59 thf(func_def_133, type, sK70: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X1 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ X0 > $o) > X4))).
% 1.42/0.59 thf(func_def_134, type, sK71: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X1 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ X0 > $o) > X3))).
% 1.42/0.59 thf(f1,axiom,(
% 1.42/0.59 ! [X2 : $tType,X1 : $tType,X4 : $tType,X0 : $tType,X7 : set @ product_prod @ X0 @ X2,X8 : set @ product_prod @ X1 @ X4] : (member @ product_prod @ (refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ (refine1665802226e_nres @ X2 > (X2 > refine1665802226e_nres @ X4) > refine1665802226e_nres @ X4) @ (product_Pair @ (refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ (refine1665802226e_nres @ X2 > (X2 > refine1665802226e_nres @ X4) > refine1665802226e_nres @ X4) @ refine463715084e_bind @ X0 @ X1 @ refine463715084e_bind @ X2 @ X4) @ (relAPP @ ((X0 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ ((X2 > refine1665802226e_nres @ X4) > refine1665802226e_nres @ X4) @ set @ product_prod @ (refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ (refine1665802226e_nres @ X2 > (X2 > refine1665802226e_nres @ X4) > refine1665802226e_nres @ X4) @ (relAPP @ refine1665802226e_nres @ X0 @ refine1665802226e_nres @ X2 @ (set @ product_prod @ ((X0 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ ((X2 > refine1665802226e_nres @ X4) > refine1665802226e_nres @ X4) > set @ product_prod @ (refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ (refine1665802226e_nres @ X2 > (X2 > refine1665802226e_nres @ X4) > refine1665802226e_nres @ X4)) @ fun_rel @ refine1665802226e_nres @ X0 @ refine1665802226e_nres @ X2 @ ((X0 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ ((X2 > refine1665802226e_nres @ X4) > refine1665802226e_nres @ X4) @ (relAPP @ X0 @ X2 @ set @ product_prod @ refine1665802226e_nres @ X0 @ refine1665802226e_nres @ X2 @ refine476890328es_rel @ X0 @ X2 @ X7)) @ (relAPP @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X4 @ set @ product_prod @ ((X0 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ ((X2 > refine1665802226e_nres @ X4) > refine1665802226e_nres @ X4) @ (relAPP @ (X0 > refine1665802226e_nres @ X1) @ (X2 > refine1665802226e_nres @ X4) @ (set @ product_prod @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X4 > set @ product_prod @ ((X0 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ ((X2 > refine1665802226e_nres @ X4) > refine1665802226e_nres @ X4)) @ fun_rel @ (X0 > refine1665802226e_nres @ X1) @ (X2 > refine1665802226e_nres @ X4) @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X4 @ (relAPP @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X4 @ set @ product_prod @ (X0 > refine1665802226e_nres @ X1) @ (X2 > refine1665802226e_nres @ X4) @ (relAPP @ X0 @ X2 @ (set @ product_prod @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X4 > set @ product_prod @ (X0 > refine1665802226e_nres @ X1) @ (X2 > refine1665802226e_nres @ X4)) @ fun_rel @ X0 @ X2 @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X4 @ X7) @ (relAPP @ X1 @ X4 @ set @ product_prod @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X4 @ refine476890328es_rel @ X1 @ X4 @ X8))) @ (relAPP @ X1 @ X4 @ set @ product_prod @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X4 @ refine476890328es_rel @ X1 @ X4 @ X8))))),
% 1.42/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_param__bind)).
% 1.42/0.59 thf(f29,axiom,(
% 1.42/0.59 ! [X2 : $tType,X0 : $tType,X1 : $tType] : (relAPP @ X2 @ X1 @ X0 = (^[X3 : (set @ product_prod @ X2 @ X1 > X0)] : (X3)))),
% 1.42/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_relAPP__def)).
% 1.42/0.59 thf(f277,conjecture,(
% 1.42/0.59 (member @ product_prod @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (product_Pair @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ refine463715084e_bind @ a @ b @ refine463715084e_bind @ c @ d) @ (relAPP @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ set @ product_prod @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (relAPP @ refine1665802226e_nres @ a @ refine1665802226e_nres @ c @ (set @ product_prod @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) > set @ product_prod @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d)) @ fun_rel @ refine1665802226e_nres @ a @ refine1665802226e_nres @ c @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (relAPP @ a @ c @ set @ product_prod @ refine1665802226e_nres @ a @ refine1665802226e_nres @ c @ refine476890328es_rel @ a @ c @ r1)) @ (relAPP @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ set @ product_prod @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (relAPP @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d) @ (set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d > set @ product_prod @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d)) @ fun_rel @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d) @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ (relAPP @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ set @ product_prod @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d) @ (relAPP @ a @ c @ (set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d > set @ product_prod @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d)) @ fun_rel @ a @ c @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ r1) @ (relAPP @ b @ d @ set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ refine476890328es_rel @ b @ d @ r2))) @ (relAPP @ b @ d @ set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ refine476890328es_rel @ b @ d @ r2))))),
% 1.42/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 1.42/0.59 thf(f278,negated_conjecture,(
% 1.42/0.59 ~(member @ product_prod @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (product_Pair @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ refine463715084e_bind @ a @ b @ refine463715084e_bind @ c @ d) @ (relAPP @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ set @ product_prod @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (relAPP @ refine1665802226e_nres @ a @ refine1665802226e_nres @ c @ (set @ product_prod @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) > set @ product_prod @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d)) @ fun_rel @ refine1665802226e_nres @ a @ refine1665802226e_nres @ c @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (relAPP @ a @ c @ set @ product_prod @ refine1665802226e_nres @ a @ refine1665802226e_nres @ c @ refine476890328es_rel @ a @ c @ r1)) @ (relAPP @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ set @ product_prod @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (relAPP @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d) @ (set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d > set @ product_prod @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d)) @ fun_rel @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d) @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ (relAPP @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ set @ product_prod @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d) @ (relAPP @ a @ c @ (set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d > set @ product_prod @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d)) @ fun_rel @ a @ c @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ r1) @ (relAPP @ b @ d @ set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ refine476890328es_rel @ b @ d @ r2))) @ (relAPP @ b @ d @ set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ refine476890328es_rel @ b @ d @ r2))))),
% 1.42/0.59 inference(negated_conjecture,[status(cth)],[f277])).
% 1.42/0.59 thf(f365,plain,(
% 1.42/0.59 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (relAPP @ X0 @ X2 @ X1 = (^[X3 : (set @ product_prod @ X0 @ X2 > X1)] : (X3)))),
% 1.42/0.59 inference(rectify,[],[f29])).
% 1.42/0.59 thf(f366,plain,(
% 1.42/0.59 ! [X1 : $tType,X0 : $tType,X2 : $tType] : ((^[Y0 : set @ product_prod @ X0 @ X2 > X1]: (Y0)) = relAPP @ X0 @ X2 @ X1)),
% 1.42/0.59 inference(fool_elimination,[],[f365])).
% 1.42/0.59 thf(f504,plain,(
% 1.42/0.59 ~(member @ product_prod @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (product_Pair @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ refine463715084e_bind @ a @ b @ refine463715084e_bind @ c @ d) @ (relAPP @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ set @ product_prod @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (relAPP @ refine1665802226e_nres @ a @ refine1665802226e_nres @ c @ (set @ product_prod @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) > set @ product_prod @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d)) @ fun_rel @ refine1665802226e_nres @ a @ refine1665802226e_nres @ c @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (relAPP @ a @ c @ set @ product_prod @ refine1665802226e_nres @ a @ refine1665802226e_nres @ c @ refine476890328es_rel @ a @ c @ r1)) @ (relAPP @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ set @ product_prod @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (relAPP @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d) @ (set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d > set @ product_prod @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d)) @ fun_rel @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d) @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ (relAPP @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ set @ product_prod @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d) @ (relAPP @ a @ c @ (set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d > set @ product_prod @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d)) @ fun_rel @ a @ c @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ r1) @ (relAPP @ b @ d @ set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ refine476890328es_rel @ b @ d @ r2))) @ (relAPP @ b @ d @ set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ refine476890328es_rel @ b @ d @ r2))))),
% 1.42/0.59 inference(rectify,[],[f278])).
% 1.42/0.59 thf(f505,plain,(
% 1.42/0.59 ~ (((member @ product_prod @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (product_Pair @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ refine463715084e_bind @ a @ b @ refine463715084e_bind @ c @ d) @ (relAPP @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ set @ product_prod @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (relAPP @ refine1665802226e_nres @ a @ refine1665802226e_nres @ c @ (set @ product_prod @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) > set @ product_prod @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d)) @ fun_rel @ refine1665802226e_nres @ a @ refine1665802226e_nres @ c @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (relAPP @ a @ c @ set @ product_prod @ refine1665802226e_nres @ a @ refine1665802226e_nres @ c @ refine476890328es_rel @ a @ c @ r1)) @ (relAPP @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ set @ product_prod @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (relAPP @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d) @ (set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d > set @ product_prod @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d)) @ fun_rel @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d) @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ (relAPP @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ set @ product_prod @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d) @ (relAPP @ a @ c @ (set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d > set @ product_prod @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d)) @ fun_rel @ a @ c @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ r1) @ (relAPP @ b @ d @ set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ refine476890328es_rel @ b @ d @ r2))) @ (relAPP @ b @ d @ set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ refine476890328es_rel @ b @ d @ r2))))) = $true)),
% 1.42/0.59 inference(fool_elimination,[],[f504])).
% 1.42/0.59 thf(f620,plain,(
% 1.42/0.59 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : set @ product_prod @ X3 @ X0,X5 : set @ product_prod @ X1 @ X2] : (member @ product_prod @ (refine1665802226e_nres @ X3 > (X3 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ (refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) @ (product_Pair @ (refine1665802226e_nres @ X3 > (X3 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ (refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) @ refine463715084e_bind @ X3 @ X1 @ refine463715084e_bind @ X0 @ X2) @ (relAPP @ ((X3 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ ((X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) @ set @ product_prod @ (refine1665802226e_nres @ X3 > (X3 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ (refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) @ (relAPP @ refine1665802226e_nres @ X3 @ refine1665802226e_nres @ X0 @ (set @ product_prod @ ((X3 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ ((X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) > set @ product_prod @ (refine1665802226e_nres @ X3 > (X3 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ (refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2)) @ fun_rel @ refine1665802226e_nres @ X3 @ refine1665802226e_nres @ X0 @ ((X3 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ ((X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) @ (relAPP @ X3 @ X0 @ set @ product_prod @ refine1665802226e_nres @ X3 @ refine1665802226e_nres @ X0 @ refine476890328es_rel @ X3 @ X0 @ X4)) @ (relAPP @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X2 @ set @ product_prod @ ((X3 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ ((X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) @ (relAPP @ (X3 > refine1665802226e_nres @ X1) @ (X0 > refine1665802226e_nres @ X2) @ (set @ product_prod @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X2 > set @ product_prod @ ((X3 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ ((X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2)) @ fun_rel @ (X3 > refine1665802226e_nres @ X1) @ (X0 > refine1665802226e_nres @ X2) @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X2 @ (relAPP @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X2 @ set @ product_prod @ (X3 > refine1665802226e_nres @ X1) @ (X0 > refine1665802226e_nres @ X2) @ (relAPP @ X3 @ X0 @ (set @ product_prod @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X2 > set @ product_prod @ (X3 > refine1665802226e_nres @ X1) @ (X0 > refine1665802226e_nres @ X2)) @ fun_rel @ X3 @ X0 @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X2 @ X4) @ (relAPP @ X1 @ X2 @ set @ product_prod @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X2 @ refine476890328es_rel @ X1 @ X2 @ X5))) @ (relAPP @ X1 @ X2 @ set @ product_prod @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X2 @ refine476890328es_rel @ X1 @ X2 @ X5))))),
% 1.42/0.59 inference(rectify,[],[f1])).
% 1.42/0.59 thf(f621,plain,(
% 1.42/0.59 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : set @ product_prod @ X3 @ X0,X5 : set @ product_prod @ X1 @ X2] : ($true = ((member @ product_prod @ (refine1665802226e_nres @ X3 > (X3 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ (refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) @ (product_Pair @ (refine1665802226e_nres @ X3 > (X3 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ (refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) @ refine463715084e_bind @ X3 @ X1 @ refine463715084e_bind @ X0 @ X2) @ (relAPP @ ((X3 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ ((X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) @ set @ product_prod @ (refine1665802226e_nres @ X3 > (X3 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ (refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) @ (relAPP @ refine1665802226e_nres @ X3 @ refine1665802226e_nres @ X0 @ (set @ product_prod @ ((X3 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ ((X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) > set @ product_prod @ (refine1665802226e_nres @ X3 > (X3 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ (refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2)) @ fun_rel @ refine1665802226e_nres @ X3 @ refine1665802226e_nres @ X0 @ ((X3 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ ((X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) @ (relAPP @ X3 @ X0 @ set @ product_prod @ refine1665802226e_nres @ X3 @ refine1665802226e_nres @ X0 @ refine476890328es_rel @ X3 @ X0 @ X4)) @ (relAPP @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X2 @ set @ product_prod @ ((X3 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ ((X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) @ (relAPP @ (X3 > refine1665802226e_nres @ X1) @ (X0 > refine1665802226e_nres @ X2) @ (set @ product_prod @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X2 > set @ product_prod @ ((X3 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ ((X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2)) @ fun_rel @ (X3 > refine1665802226e_nres @ X1) @ (X0 > refine1665802226e_nres @ X2) @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X2 @ (relAPP @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X2 @ set @ product_prod @ (X3 > refine1665802226e_nres @ X1) @ (X0 > refine1665802226e_nres @ X2) @ (relAPP @ X3 @ X0 @ (set @ product_prod @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X2 > set @ product_prod @ (X3 > refine1665802226e_nres @ X1) @ (X0 > refine1665802226e_nres @ X2)) @ fun_rel @ X3 @ X0 @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X2 @ X4) @ (relAPP @ X1 @ X2 @ set @ product_prod @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X2 @ refine476890328es_rel @ X1 @ X2 @ X5))) @ (relAPP @ X1 @ X2 @ set @ product_prod @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X2 @ refine476890328es_rel @ X1 @ X2 @ X5))))))),
% 1.42/0.59 inference(fool_elimination,[],[f620])).
% 1.42/0.59 thf(f627,plain,(
% 1.42/0.59 (((member @ product_prod @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (product_Pair @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ refine463715084e_bind @ a @ b @ refine463715084e_bind @ c @ d) @ (relAPP @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ set @ product_prod @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (relAPP @ refine1665802226e_nres @ a @ refine1665802226e_nres @ c @ (set @ product_prod @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) > set @ product_prod @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d)) @ fun_rel @ refine1665802226e_nres @ a @ refine1665802226e_nres @ c @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (relAPP @ a @ c @ set @ product_prod @ refine1665802226e_nres @ a @ refine1665802226e_nres @ c @ refine476890328es_rel @ a @ c @ r1)) @ (relAPP @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ set @ product_prod @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (relAPP @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d) @ (set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d > set @ product_prod @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d)) @ fun_rel @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d) @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ (relAPP @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ set @ product_prod @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d) @ (relAPP @ a @ c @ (set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d > set @ product_prod @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d)) @ fun_rel @ a @ c @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ r1) @ (relAPP @ b @ d @ set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ refine476890328es_rel @ b @ d @ r2))) @ (relAPP @ b @ d @ set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ refine476890328es_rel @ b @ d @ r2))))) != $true)),
% 1.42/0.59 inference(flattening,[],[f505])).
% 1.42/0.59 thf(f738,plain,(
% 1.42/0.59 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (relAPP @ X1 @ X2 @ X0 = (^[Y0 : set @ product_prod @ X1 @ X2 > X0]: (Y0)))),
% 1.42/0.59 inference(rectify,[],[f366])).
% 1.42/0.59 thf(f783,plain,(
% 1.42/0.59 (((member @ product_prod @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (product_Pair @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ refine463715084e_bind @ a @ b @ refine463715084e_bind @ c @ d) @ (relAPP @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ set @ product_prod @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (relAPP @ refine1665802226e_nres @ a @ refine1665802226e_nres @ c @ (set @ product_prod @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) > set @ product_prod @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d)) @ fun_rel @ refine1665802226e_nres @ a @ refine1665802226e_nres @ c @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (relAPP @ a @ c @ set @ product_prod @ refine1665802226e_nres @ a @ refine1665802226e_nres @ c @ refine476890328es_rel @ a @ c @ r1)) @ (relAPP @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ set @ product_prod @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (relAPP @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d) @ (set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d > set @ product_prod @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d)) @ fun_rel @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d) @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ (relAPP @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ set @ product_prod @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d) @ (relAPP @ a @ c @ (set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d > set @ product_prod @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d)) @ fun_rel @ a @ c @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ r1) @ (relAPP @ b @ d @ set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ refine476890328es_rel @ b @ d @ r2))) @ (relAPP @ b @ d @ set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ refine476890328es_rel @ b @ d @ r2))))) != $true)),
% 1.42/0.59 inference(cnf_transformation,[],[f627])).
% 1.42/0.59 thf(f794,plain,(
% 1.42/0.59 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : ((relAPP @ X1 @ X2 @ X0 = (^[Y0 : set @ product_prod @ X1 @ X2 > X0]: (Y0)))) )),
% 1.42/0.59 inference(cnf_transformation,[],[f738])).
% 1.42/0.59 thf(f805,plain,(
% 1.42/0.59 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X4 : set @ product_prod @ X3 @ X0,X5 : set @ product_prod @ X1 @ X2] : (($true = ((member @ product_prod @ (refine1665802226e_nres @ X3 > (X3 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ (refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) @ (product_Pair @ (refine1665802226e_nres @ X3 > (X3 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ (refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) @ refine463715084e_bind @ X3 @ X1 @ refine463715084e_bind @ X0 @ X2) @ (relAPP @ ((X3 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ ((X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) @ set @ product_prod @ (refine1665802226e_nres @ X3 > (X3 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ (refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) @ (relAPP @ refine1665802226e_nres @ X3 @ refine1665802226e_nres @ X0 @ (set @ product_prod @ ((X3 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ ((X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) > set @ product_prod @ (refine1665802226e_nres @ X3 > (X3 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ (refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2)) @ fun_rel @ refine1665802226e_nres @ X3 @ refine1665802226e_nres @ X0 @ ((X3 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ ((X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) @ (relAPP @ X3 @ X0 @ set @ product_prod @ refine1665802226e_nres @ X3 @ refine1665802226e_nres @ X0 @ refine476890328es_rel @ X3 @ X0 @ X4)) @ (relAPP @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X2 @ set @ product_prod @ ((X3 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ ((X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) @ (relAPP @ (X3 > refine1665802226e_nres @ X1) @ (X0 > refine1665802226e_nres @ X2) @ (set @ product_prod @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X2 > set @ product_prod @ ((X3 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ ((X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2)) @ fun_rel @ (X3 > refine1665802226e_nres @ X1) @ (X0 > refine1665802226e_nres @ X2) @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X2 @ (relAPP @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X2 @ set @ product_prod @ (X3 > refine1665802226e_nres @ X1) @ (X0 > refine1665802226e_nres @ X2) @ (relAPP @ X3 @ X0 @ (set @ product_prod @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X2 > set @ product_prod @ (X3 > refine1665802226e_nres @ X1) @ (X0 > refine1665802226e_nres @ X2)) @ fun_rel @ X3 @ X0 @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X2 @ X4) @ (relAPP @ X1 @ X2 @ set @ product_prod @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X2 @ refine476890328es_rel @ X1 @ X2 @ X5))) @ (relAPP @ X1 @ X2 @ set @ product_prod @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X2 @ refine476890328es_rel @ X1 @ X2 @ X5))))))) )),
% 1.42/0.59 inference(cnf_transformation,[],[f621])).
% 1.42/0.59 thf(f822,plain,(
% 1.42/0.59 ($true != ((member @ product_prod @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (product_Pair @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ refine463715084e_bind @ a @ b @ refine463715084e_bind @ c @ d) @ ((^[Y0 : set @ product_prod @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) > set @ product_prod @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d)]: (Y0)) @ ((^[Y0 : set @ product_prod @ refine1665802226e_nres @ a @ refine1665802226e_nres @ c > set @ product_prod @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) > set @ product_prod @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d)]: (Y0)) @ fun_rel @ refine1665802226e_nres @ a @ refine1665802226e_nres @ c @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ ((^[Y0 : set @ product_prod @ a @ c > set @ product_prod @ refine1665802226e_nres @ a @ refine1665802226e_nres @ c]: (Y0)) @ refine476890328es_rel @ a @ c @ r1)) @ ((^[Y0 : set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d > set @ product_prod @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d)]: (Y0)) @ ((^[Y0 : set @ product_prod @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d) > set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d > set @ product_prod @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d)]: (Y0)) @ fun_rel @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d) @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ ((^[Y0 : set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d > set @ product_prod @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d)]: (Y0)) @ ((^[Y0 : set @ product_prod @ a @ c > set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d > set @ product_prod @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d)]: (Y0)) @ fun_rel @ a @ c @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ r1) @ ((^[Y0 : set @ product_prod @ b @ d > set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d]: (Y0)) @ refine476890328es_rel @ b @ d @ r2))) @ ((^[Y0 : set @ product_prod @ b @ d > set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d]: (Y0)) @ refine476890328es_rel @ b @ d @ r2))))))),
% 1.42/0.59 inference(definition_unfolding,[],[f783,f794,f794,f794,f794,f794,f794,f794,f794,f794])).
% 1.42/0.59 thf(f826,plain,(
% 1.42/0.59 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X4 : set @ product_prod @ X3 @ X0,X5 : set @ product_prod @ X1 @ X2] : (($true = ((member @ product_prod @ (refine1665802226e_nres @ X3 > (X3 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ (refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) @ (product_Pair @ (refine1665802226e_nres @ X3 > (X3 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ (refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) @ refine463715084e_bind @ X3 @ X1 @ refine463715084e_bind @ X0 @ X2) @ ((^[Y0 : set @ product_prod @ ((X3 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ ((X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) > set @ product_prod @ (refine1665802226e_nres @ X3 > (X3 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ (refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2)]: (Y0)) @ ((^[Y0 : set @ product_prod @ refine1665802226e_nres @ X3 @ refine1665802226e_nres @ X0 > set @ product_prod @ ((X3 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ ((X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) > set @ product_prod @ (refine1665802226e_nres @ X3 > (X3 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ (refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2)]: (Y0)) @ fun_rel @ refine1665802226e_nres @ X3 @ refine1665802226e_nres @ X0 @ ((X3 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ ((X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) @ ((^[Y0 : set @ product_prod @ X3 @ X0 > set @ product_prod @ refine1665802226e_nres @ X3 @ refine1665802226e_nres @ X0]: (Y0)) @ refine476890328es_rel @ X3 @ X0 @ X4)) @ ((^[Y0 : set @ product_prod @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X2 > set @ product_prod @ ((X3 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ ((X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2)]: (Y0)) @ ((^[Y0 : set @ product_prod @ (X3 > refine1665802226e_nres @ X1) @ (X0 > refine1665802226e_nres @ X2) > set @ product_prod @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X2 > set @ product_prod @ ((X3 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ ((X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2)]: (Y0)) @ fun_rel @ (X3 > refine1665802226e_nres @ X1) @ (X0 > refine1665802226e_nres @ X2) @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X2 @ ((^[Y0 : set @ product_prod @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X2 > set @ product_prod @ (X3 > refine1665802226e_nres @ X1) @ (X0 > refine1665802226e_nres @ X2)]: (Y0)) @ ((^[Y0 : set @ product_prod @ X3 @ X0 > set @ product_prod @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X2 > set @ product_prod @ (X3 > refine1665802226e_nres @ X1) @ (X0 > refine1665802226e_nres @ X2)]: (Y0)) @ fun_rel @ X3 @ X0 @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X2 @ X4) @ ((^[Y0 : set @ product_prod @ X1 @ X2 > set @ product_prod @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X2]: (Y0)) @ refine476890328es_rel @ X1 @ X2 @ X5))) @ ((^[Y0 : set @ product_prod @ X1 @ X2 > set @ product_prod @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X2]: (Y0)) @ refine476890328es_rel @ X1 @ X2 @ X5))))))) )),
% 1.42/0.59 inference(definition_unfolding,[],[f805,f794,f794,f794,f794,f794,f794,f794,f794,f794])).
% 1.42/0.59 thf(f841,plain,(
% 1.42/0.59 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X4 : set @ product_prod @ X3 @ X0,X5 : set @ product_prod @ X1 @ X2] : ((((member @ product_prod @ (refine1665802226e_nres @ X3 > (X3 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ (refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) @ (product_Pair @ (refine1665802226e_nres @ X3 > (X3 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ (refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) @ refine463715084e_bind @ X3 @ X1 @ refine463715084e_bind @ X0 @ X2) @ (fun_rel @ refine1665802226e_nres @ X3 @ refine1665802226e_nres @ X0 @ ((X3 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ ((X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) @ (refine476890328es_rel @ X3 @ X0 @ X4) @ (fun_rel @ (X3 > refine1665802226e_nres @ X1) @ (X0 > refine1665802226e_nres @ X2) @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X2 @ (fun_rel @ X3 @ X0 @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X2 @ X4 @ (refine476890328es_rel @ X1 @ X2 @ X5)) @ (refine476890328es_rel @ X1 @ X2 @ X5))))) = $true)) )),
% 1.42/0.59 inference(beta-eta_normalization,[],[f826])).
% 1.42/0.59 thf(f851,plain,(
% 1.42/0.59 (((member @ product_prod @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (product_Pair @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ refine463715084e_bind @ a @ b @ refine463715084e_bind @ c @ d) @ (fun_rel @ refine1665802226e_nres @ a @ refine1665802226e_nres @ c @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (refine476890328es_rel @ a @ c @ r1) @ (fun_rel @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d) @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ (fun_rel @ a @ c @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ r1 @ (refine476890328es_rel @ b @ d @ r2)) @ (refine476890328es_rel @ b @ d @ r2))))) != $true)),
% 1.42/0.59 inference(beta-eta_normalization,[],[f822])).
% 1.42/0.59 thf(f852,plain,(
% 1.42/0.59 $false),
% 1.42/0.59 inference(forward_subsumption_resolution,[],[f851,f841])).
% 1.42/0.59 % SZS output end Proof for theBenchmark
% 1.42/0.59 % (2592191)------------------------------
% 1.42/0.59 % (2592191)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.59 % (2592191)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.59 % (2592191)CaDiCaL version: 2.1.3
% 1.42/0.59 % (2592191)Termination reason: Refutation
% 1.42/0.59 % (2592191)Time elapsed: 0.070 s
% 1.42/0.59 % (2592191)Peak memory usage: 14 MB
% 1.42/0.59 % (2592191)Instructions burned: 147 (million)
% 1.42/0.59 % (2592157)Success in time 0.254 s
% 1.42/0.59 % Vampire exiting
%------------------------------------------------------------------------------